Quadratic Vertex Word Problems

Imagine walking along a hiking path in the shape of a parabola. You keep walking and stop only at 4 points in time.

You have been walking on what seems like a straight part of the path for a long time and when passing by a big tree, you sit in its shades and rest for a bit.

You keep walking and come upon a clear stream, you take another break while drinking the sweetest water you've ever tasted.

You continue walking and the road becomes curvier. Finally you stop again at a point where the path seems to change direction. There is a rest station there.

You make a final stop when you see a big rock and decided to lie on it for a brief moment.